x+(1/3x+3)=180

Solution for x+(1/3x+3)=180 equation:

x+(1/3x+3)=180

We move all terms to the left:

x+(1/3x+3)-(180)=0


Domain of the equation: 3x+3)!=0

x∈R


We get rid of parentheses

x+1/3x+3-180=0

We multiply all the terms by the denominator


x*3x+3*3x-180*3x+1=0

Wy multiply elements

3x^2+9x-540x+1=0

We add all the numbers together, and all the variables

3x^2-531x+1=0

a = 3; b = -531; c = +1;
Δ = b2-4ac
Δ = -5312-4·3·1
Δ = 281949
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-531)-\sqrt{281949}}{2*3}=\frac{531-\sqrt{281949}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-531)+\sqrt{281949}}{2*3}=\frac{531+\sqrt{281949}}{6}
$